Results 31 to 40 of about 3,324,527 (305)
Proceedings of the American Mathematical Society, 1962 Let \(F^*\) be the multiplicative group of non-zero elements of \(\mathrm{GF}(p^n)\) where \(p\) is a prime; set \(p^n-1 = rs\) where \((r, s) = 1\), \(r < s\) and \(r\not\equiv 1 \bmod p\). \(F^*\) has subgroups \(Y, Z\) of orders \(r, s\) respectively and every element \(\xi\) of \(F^*\) can be expressed uniquely in the form \(\xi = \eta\zeta\) with \
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THEORETICAL ASSUMPTIONS FOR AN INTRODUCTION TO ELLIPTIC CURVE CRYPTOGRAPHY
STED Journal, 2023 Understanding elliptic curves contributed to solving mathematical problems in number theory that had been unsolved for centuries. Elliptic curves were also used in solving one of the millennial problems, which is Fermat's last theorem.
Ognjen Milivojević, Boris Damjanović
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FINITE UNDECIDABILITY IN NIP FIELDS
The Journal of Symbolic Logic, 2023 AbstractA field K in a ring language $\mathcal {L}$ is finitely undecidable if $\mbox {Cons}(T)$ is undecidable for every nonempty finite $T \subseteq {\mathtt{Th}}(K; \mathcal {L})$ . We extend a construction of Ziegler and (among other results) use a first-order classification of Anscombe and Jahnke to prove every NIP henselian nontrivially ...
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Superregular Matrices over Finite Fields
MathematicsA trivially zero minor of a matrix is a minor having all its terms in the Leibniz formula equal to zero. A matrix is superregular if all of its minors that are not trivially zero are nonzero.
Paulo Almeida +2 more
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Pseudo-Chebyshev Functions Over Finite Fields
IEEE Open Journal of Circuits and SystemsIn this paper, we introduce the notion of pseudo-Chebyshev functions over finite fields. In brief, such functions correspond to a generalization of the $n$ -th Chebyshev polynomial, where $n$ is not restricted to integer values, but can take on any ...
Juliano B. Lima +2 more
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Parallel machine arithmetic for recurrent number systems in non-quadratic fields [PDF]
Компьютерная оптика, 2020 The paper proposes a new method of synthesis of computer arithmetic systems for "error-free" parallel calculations. The difference between the proposed approach and calculations in traditional systems of Residue Number Systems for the direct sum of ...
Vladimir Chernov
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A note on some Picard curves over finite fields
, 2015 In this note we provide a complete classification for the Newton polygon of the Picard curvesy3=x4-xandy3=x4-1 defined over a finite field of characteristic p>3. In fact, we complete the results obtained in [19].
Tafazolian, Saeed, Kazemifard, Ahmad
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Distribution of constant terms of irreducible polynomials in ℤₚ[x] whose degree is a product of two distinct odd primes [PDF]
Notes on Number Theory and Discrete MathematicsWe obtain explicit formulas for the number of monic irreducible polynomials with prescribed constant term and degree q₁q₂ over a finite field, where q₁ and q₂ are distinct odd primes. These formulas are derived from work done by Yucas.
Sarah C. Cobb +4 more
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A Small Subgroup Attack on Bitcoin Address Generation
Mathematics, 2020 We show how a small subgroup confinement-like attack may be mounted on the Bitcoin addresses generation protocol, by inspecting a special subgroup of the group associated to point multiplication.
Massimiliano Sala +2 more
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Powers in finite fields. [PDF]
, 2022 This work deals with the powers of elements of finite fields. The proof of the classical criterion of Euler for squares in finite fields of prime order is presented.
Bandžiulis, Kastytis,
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